分红对期指的影响20250509

Quantitative Models and Construction Methods - Model Name: Theoretical Pricing Model for Stock Index Futures Model Construction Idea: This model aims to calculate the theoretical price of stock index futures by considering the impact of dividends and risk-free interest rates under no-arbitrage conditions [35][36] Model Construction Process: 1. Discrete Dividend Distribution: - Assume the futures price at time $t$ is $F_t$, the spot price is $S_t$, and the futures contract expires at $T$. The present value of dividends during $T-t$ is $D$, and the risk-free rate during $T-t$ is $r$. - If there are $m$ dividend payments at times $t_1, t_2, ..., t_m$, with amounts $D_1, D_2, ..., D_m$, the present value of dividends is: $\mathbf{D} = \sum_{\mathrm{i=1}}^{\mathrm{m}} \mathbf{D}_{\mathrm{i}} / (1 + \phi)$ where $\phi$ is the risk-free rate between two dividend payments. - The theoretical futures price is: $F_t = (S_t - D)(1 + r)$ [35] 2. Continuous Dividend Distribution: - When dividends are distributed continuously, the model assumes the annualized dividend yield is $d$, and the annualized risk-free rate is $r$. The theoretical futures price is: $F_t = S_t e^{(r-d)(T-t)}$ [36] Quantitative Factors and Construction Methods - Factor Name: Dividend Impact Factor Factor Construction Idea: This factor estimates the impact of dividends on stock index futures pricing by predicting the dividend points for index components and their contribution to the index [12][27] Factor Construction Process: 1. Estimate Net Profit: Use available financial data in the following order of priority: annual reports, quick reports, earnings warnings, trailing twelve-month (TTM) net profit, or analysts' forecasts [27][31] 2. Calculate Total Dividends: Assume the dividend payout ratio remains constant for companies with historical dividends. For companies with no prior dividends or negative profits, assume zero dividends [31] 3. Calculate Dividend Impact on Index: - Dividend yield: $\text{Tax-adjusted dividends} / \text{Latest market cap}$ - Dividend points: $\text{Stock weight} \times \text{Dividend yield}$ - Adjust stock weights using the formula: $w_{it} = \frac{w_{i0} \times (1 + R)}{\sum_{1}^{n} w_{i0} \times (1 + R)}$ where $w_{i0}$ is the initial weight, and $R$ is the stock's return [29] 4. Predict Impact on Futures Contracts: Aggregate the dividend points for all components before the contract's settlement date [33] Model Backtesting Results - Theoretical Pricing Model: - Annualized hedging costs (excluding dividends) for May contracts: - SSE 50: 0.27% - CSI 300: 7.07% - CSI 500: 15.59% - CSI 1000: 18.88% [12][13][15][16] Factor Backtesting Results - Dividend Impact Factor: - Remaining impact of dividends on May contracts: - SSE 50: 0.01% - CSI 300: 0.02% - CSI 500: 0.04% - CSI 1000: 0.06% [17]